Functional Lifting 2.0: Efficient Convexifications for Imaging and Vision

  • Cremers, Daniel (Principal Investigator (PI))
  • Lellmann, Jan (Principal Investigator (PI))
  • Möller, Michael (Principal Investigator (PI))

Project: DFG ProjectsDFG Individual Projects

Project Details

Description

One of the most versatile and powerful tools for solving computer vision and image processing problems is the class of energy-based methods. The basic idea is to associate with every conceivable solution a cost - or energy - in such a way that low energy values correspond to good solutions. Unfortunately, most practically relevant problems inherently lead to non-convex energy functions, so that the computation of global minimizers becomes very challenging. Consequently, the solution quality in classical local minimization methods heavily depends on the initialization and the particular choice of algorithm. In this project, we will develop global methods that rely on a convexification of non-convex energies in high-dimensional spaces by means of functional lifting in order to find globally optimal solutions. Existing approaches implemented this lifting by discretizing the range into labels, ultimately limiting the solution accuracy. In contrast, this project will extend the applicability of recent sublabel-accurate lifting methods that greatly reduce the extra cost of obtaining an approximate global solution and allow to gradually take into account the non-convexities while exploiting convex parts in the energy. This allows to develop solvers that scale gracefully with the non-convexity of the problem, and allow to efficiently compute close-to-globally optimal solutions on a wide range of optimization problems.
Statusfinished
Effective start/end date01.01.1831.12.22

Collaborative partners

  • Technical University of Munich (Joint applicant, Co-PI) (lead)
  • University of Siegen (Joint applicant, Co-PI)

UN Sustainable Development Goals

In 2015, UN member states agreed to 17 global Sustainable Development Goals (SDGs) to end poverty, protect the planet and ensure prosperity for all. This project contributes towards the following SDG(s):

  • SDG 9 - Industry, Innovation, and Infrastructure

Research Areas and Centers

  • Academic Focus: Biomedical Engineering

DFG Research Classification Scheme

  • 409-05 Interactive and Intelligent Systems, Image and Language Processing, Computer Graphics and Visualisation

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